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Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions

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  • Shelby Haberman
  • Sandip Sinharay
  • Kyong Chon

Abstract

Residual analysis (e.g. Hambleton & Swaminathan, Item response theory: principles and applications, Kluwer Academic, Boston, 1985 ; Hambleton, Swaminathan, & Rogers, Fundamentals of item response theory, Sage, Newbury Park, 1991 ) is a popular method to assess fit of item response theory (IRT) models. We suggest a form of residual analysis that may be applied to assess item fit for unidimensional IRT models. The residual analysis consists of a comparison of the maximum-likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve. The large sample distribution of the residual is proved to be standardized normal when the IRT model fits the data. We compare the performance of our suggested residual to the standardized residual of Hambleton et al. (Fundamentals of item response theory, Sage, Newbury Park, 1991 ) in a detailed simulation study. We then calculate our suggested residuals using data from an operational test. The residuals appear to be useful in assessing the item fit for unidimensional IRT models. Copyright The Psychometric Society 2013

Suggested Citation

  • Shelby Haberman & Sandip Sinharay & Kyong Chon, 2013. "Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 417-440, July.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:3:p:417-440
    DOI: 10.1007/s11336-012-9305-1
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    References listed on IDEAS

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    1. J. C. Naylor & A. F. M. Smith, 1982. "Applications of a Method for the Efficient Computation of Posterior Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 214-225, November.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    4. Paul Holland, 1990. "The Dutch Identity: A new tool for the study of item response models," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 5-18, March.
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    Cited by:

    1. Peter W. Rijn & Usama S. Ali, 2018. "A Generalized Speed–Accuracy Response Model for Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 109-131, March.
    2. Scott Monroe, 2021. "Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 374-398, June.
    3. Gerhard Tutz, 2022. "Item Response Thresholds Models: A General Class of Models for Varying Types of Items," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1238-1269, December.
    4. Yang Liu & Ji Seung Yang & Alberto Maydeu-Olivares, 2019. "Restricted Recalibration of Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 529-553, June.
    5. Yi-Hsuan Lee & Charles Lewis, 2021. "Monitoring Item Performance With CUSUM Statistics in Continuous Testing," Journal of Educational and Behavioral Statistics, , vol. 46(5), pages 611-648, October.
    6. Jochen Ranger & Kay Brauer, 2022. "On the Generalized S − X 2 –Test of Item Fit: Some Variants, Residuals, and a Graphical Visualization," Journal of Educational and Behavioral Statistics, , vol. 47(2), pages 202-230, April.

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